Build the Aromatic Foundation: In a large Dutch oven or heavy-bottomed pot, heat 1/4 cup of the extra virgin olive oil over medium heat. Add the onion, leek, and fennel. Sauté for 8-10 minutes, stirring occasionally, until softened and fragrant but not browned. Add the smashed garlic and saffron threads and cook for one minute more until aromatic.
Create the Golden Broth: Stir in the grated tomatoes and cook for 2 minutes to meld the flavors. Pour in the water (or broth), add the bouquet garni, and season with a few grinds of black pepper. Bring the mixture to a lively simmer.
Simmer the Hearty Vegetables: Add the scrubbed potato chunks and carrot rounds to the pot. Reduce the heat to maintain a gentle simmer, cover, and cook for 15 minutes, or until the vegetables are just beginning to become tender.
Prepare and Poach the Fish: While the vegetables cook, gently place the mixed fish pieces into the center of a large piece of cheesecloth and tie it loosely with kitchen twine to create a "fish pouch." This keeps the fish intact for serving and prevents bones from flaking into the soup.
Infuse the Seafood and Beans: Gently lower the fish pouch into the simmering broth. Add the rinsed cannellini beans and the zucchini slices to the pot around the pouch. Return the soup to a simmer and cook, uncovered, for 10-12 minutes, or until the fish is opaque and cooked through.
Finish with Shellfish and Acidity: Add the cleaned mussels to the pot, nestling them into the broth. Cover the pot and cook for 3-5 minutes, until all the mussels have opened. Discard any that remain closed. Turn off the heat.
Deconstruct and Serve: Carefully remove the bouquet garni and the fish pouch. Open the pouch and arrange the large pieces of fish on a platter alongside the potatoes, carrots, and other vegetables, using a slotted spoon. Stir the fresh lemon juice and the remaining 1/4 cup of extra virgin olive oil into the broth left in the pot.
Plating: Ladle the fragrant, golden broth into individual soup bowls. Garnish generously with fresh parsley or dill. Serve immediately, with the platter of fish and vegetables at the center of the table for guests to share.